Prologue - My First Gun
Chapter 1 - Blindsided
Chapter 2 - Cleaning Up the Berg
Chapter 3 - Best Minion Ever
Chapter 4 - The Road to Sanctuary
Chapter 5 - Plan B
Chapter 6 - Hunting the Firehawk
Chapter 7 - A Dam Fine Rescue
Chapter 8 - A Train to Catch
Chapter 9 - Rising Action
Chapter 10 - Bright Lights, Flying City
Chapter 11 - Wildlife Preservation
Chapter 12 - The Once and Future Slab
Chapter 13 - The Man Who Would Be Jack
Chapter 14 - Where Angels Fear to Tread
Chapter 15 - Where Angels Fear to Tread 2
Chapter 16 - Toil and Trouble
Chapter 17 - Data Mining
Chapter 18 - Talon of God
There are a series of main or 'story' missions that are fed to you one after the other starting with the My First Gun mission. Completing all 19 story missions (prologue + 18 chapters) will officially beat the game, roll the game credits at the end and unlock True Vault Hunter Mode, a chance to run through the game at a higher difficulty setting while keeping all the gear and skill points you earned in your first run through the game.
The story missions will get more and more difficult as you go along and each is rated to be taken on at a recommended character level. If your attained character level is around or equal to the recommended mission level, that mission will be marked in the game as 'Normal' and you should be able to defeat the enemies you encounter in that mission without too much difficulty.
If however the mission is rated considerably higher than your current character level, the mission will be very difficult or even impossible to complete. In this situation, the mission will be marked in the game as 'Tough' or 'Impossible' respectively to let you know what's in store for you.
Taking on and completing only the story missions will not allow you to accumulate enough XP to keep all the story missions that follow marked as 'Normal'. In other words, your character level will quickly fall behind the recommended level to take on the next story mission.
In order to level up enough, you will have to complete many optional 'side' missions. There are a total of 109 side missions in the game most of which are much easier to complete than the story missions. Completing side missions will allow you to accumulate enough XP to level up to recommended character levels to continue pushing through the story mission line.
Hence, maintaining a good mix of story missions and optional side missions as you go through the game is the key to surviving this epic journey without too much frustration. Note that it is not necessary to complete all the side missions to beat the game and that certain missions will reward you with certain weapons, some of which may be more useful to some character classes than others.
My Borderlands 2 video walkthrough will show you how to complete all the story missions as well as list and schedule the 74 optional side missions I personally think are necessary and/or highly beneficial to beating the game comfortably going solo as Zero the Assassin.